Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials

Details Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials

2002-05-31

arxiv.org/abs/math/0205324v3

Duke Math. J. 125 (2004), no. 3, 549--588.

Mathematics

Quantum Algebra

31 pages

Scientific paper

The fusion rule gives the dimensions of spaces of conformal blocks in the WZW theory. We prove a dimension formula similar to the fusion rulefor spaces of coinvariants of affine Lie algebras g^. An equivalence of filtered spaces is established between spaces of coinvariants of two objects: highest weight g^-modules and tensor products of finite-dimensional evaluation representations of g\otimes\C[t]. In the sl_2 case we prove that their associated graded spaces are isomorphic to the spaces of coinvariants of fusion products, and that their Hilbert polynomials are the level-restricted Kostka polynomials.

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